"There are no plans to shift commemorations _ they will still be celebrated on the actual dates _ but it doesn't seem fair that where workers are entitled to a day off they are sometimes missing out.''
Mr Clark said a law change would not have a negative affect on employers because they already budgeted for 11 statutory holidays.
"The bill makes sense and, while I hate to admit it, the Australians already 'Monday-ise' their public holidays. There's no reason Kiwis should continue to miss out.''
The legislation has a long way to go before it can become law, and Mr Clark would need a majority of support from around Parliament just to get the bill past its first reading.
Prime Minister John Key said the National Party caucus would have to discuss whether to support a law change.
"When it was an issue last year I said I'd get some advice on it, I haven't actually seen that advice yet,'' he said.
"I'm not sure it comes up in any relevant way in the short term, but it's something the caucus can consider.''
National's Simon O'Connor was the other MP to have success in today's ballot, with his Joint Family Homes Repeal Bill being drawn.
The bill would repeal a 1964 law that protected the family home, which had been surpassed by more recent legislation that provides the same protection.
The members' bill ballot is seen as something of a parliamentary lottery, and is only held when there is space on Parliament's order paper for another bill. The most recent ballot before today's was held in November, 2010.
Traditionally the bills have a low success rate in being passed into law, although there have been several well-known cases of success.
Among the most famous was Labour MP Fran Wilde's Homosexual Law Reform Bill, which decriminalised male homosexuality and was voted into law by a slim majority in 1986.
Another successful bill was Green MP Sue Bradford's controversial Crimes (Substituted Section 59) Amendment Bill - more often referred to as the "anti-smacking bill'' - which passed in 2007.